Transpositional modulation systems and methods

ABSTRACT

Systems and methods for transpositional modulation and demodulation are provided. One such method for generating a signal includes the steps of providing a look-up table having a plurality of quarter-cycle waveforms, each of said quarter-cycle waveforms associated with a respective input level; receiving an input signal; and outputting quarter-cycle waveforms associated with levels of the received input signal. Systems for transpositional modulation are also provided. One such system for generating a signal includes a look-up table having a plurality of quarter-cycle waveforms. Each of the quarter-cycle waveforms are associated with a respective input level, and the look-up table is configured to receive an input signal, and output quarter-cycle waveforms associated with levels of the received input signal.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation application of U.S. patentapplication Ser. No. 15/060,255, filed Mar. 3, 2016, which is acontinuation application of U.S. patent application Ser. No. 14/668,536,filed Mar. 25, 2015, now U.S. Pat. No. 9,379,925, issued Jun. 28, 2016,which in turn is a divisional of U.S. application Ser. No. 13/841,889,filed Mar. 15, 2013, now U.S. Pat. No. 9,014,293, issued Apr. 21, 2015.

FIELD OF THE DISCLOSURE

The present disclosure is generally related to signal processing, andmore particularly is related to systems and methods for generatingtranspositional modulation signals, and for demodulating transpositionalmodulation signals.

BACKGROUND OF THE DISCLOSURE

Existing transmission systems, whether carrying voice, video or data,have bandwidth limits imposed by domestic and world regulatory agenciescontrolling the utilization of the frequency spectra. Carrier modulationmethods have evolved from the original Amplitude Modulation to presentmethods combining two or more carriers with Amplitude, Frequency orPhase modulations in various combinations. Advanced carrier modulationmethods were developed to maximize energy throughout the assignedchannel bandwidth thus providing the greatest available informationbandwidth for the assigned communication channel.

A new fundamental carrier modulation was developed and first patented(see, e.g., U.S. Pat. No. 4,613,974 to Vokac et al., incorporated in itsentirety herein) that applies a new type of carrier modulation that doesnot interfere with amplitude, frequency and/or phase modulationcoexisting on the same carrier signal.

The concept of Transpositional (TM) Modulation was based on an earlierconcept of how to add information to a carrier signal without affectingits amplitude, frequency or phase (see, e.g., U.S. Pat. No. 4,613,974 toVokac et al., incorporated in its entirety herein). By producing aninflection as shown below, information can be conveyed by the carriersignal. This method is not detected by existing de-modulators ofamplitude, frequency or phase modulation.

Using the previously patented method of generation the followingtime-domain waveform is generated with the inflections exaggerated forclarity. In real-world applications, the inflections are not visible.

A deficiency of earlier methods of generating this type of waveform is asmall amplitude variation that required removal by an adjusting circuit.For example, FIG. 1 is an illustration of a TM Modulated signal 100generated in accordance with the prior art techniques taught by U.S.Pat. No. 4,613,974. As can be seen, an amplitude variation error existsbetween negative peaks 101 and 102.

Thus, a heretofore unaddressed need exists in the industry to addressthe aforementioned deficiencies and inadequacies.

SUMMARY OF THE DISCLOSURE

Embodiments of the present disclosure provide methods and systems forgenerating modulated signals, and for demodulating signals. In oneembodiment, a method of generating a signal is provided that includesthe steps of: providing a look-up table having a plurality ofquarter-cycle waveforms, each of the quarter-cycle waveforms associatedwith a respective input level; receiving an input signal; and outputtingquarter-cycle waveforms associated with levels of the received inputsignal.

In another embodiment, a method of generating a signal is provided thatincludes the steps of: receiving a carrier signal; receiving an inputsignal; generating quarter-cycle waveforms based on the input signal;and assembling the generated quarter-cycle waveforms into a continuousoutput signal, wherein the output signal includes a first inflectionbetween adjacent quarter-cycles forming a segment of the output signalbetween a first negative peak and a positive peak, and wherein theoutput signal includes a second inflection between adjacentquarter-cycles forming a segment of the output signal between thepositive peak and a second negative peak, wherein the first and secondinflections represent a level of said input signal.

In another embodiment, a method for generating a modulated signal isprovided that includes the steps of: receiving a carrier signal;receiving an input signal; generating a third harmonic sideband based onthe received signals; and frequency-shifting the third harmonic sidebandto the frequency of the received carrier signal.

In yet another embodiment, a method of demodulating a signal is providedthat includes the steps of: adding a third harmonic to the modulatedsignal; detecting a peak amplitude of the modulated signal plus thirdharmonic; generating a reference ramp when a peak amplitude is detected;detecting an inflection in the modulated signal plus third harmonic;sampling the reference ramp when an inflection is detected; and holdingand outputting the sampled value.

In another embodiment, a method of demodulating a signal is providedthat includes the steps of: filtering out all but the third harmoniccomponent from the modulated signal; and detecting the phase of thethird harmonic component.

In still another embodiment, a method of demodulating a signal isprovided that includes the steps of: converting the modulated signal toa digital signal; and performing a fast Fourier transform on the digitalsignal.

In yet another embodiment, a system for generating a signal is provided.The system includes a look-up table having a plurality of quarter-cyclewaveforms. Each of the quarter-cycle waveforms are associated with arespective input level. The look-up table is configured to receive aninput signal, and output quarter-cycle waveforms associated with levelsof the received input signal.

In another embodiment, a system for generating a signal is provided thatincludes a waveform generator configured to generate quarter-cyclewaveforms based on a received carrier signal and a received inputsignal. An analog gate is included for assembling the generatedquarter-cycle waveforms into a continuous output signal, wherein theoutput signal includes a first inflection between adjacentquarter-cycles forming a segment of the output signal between a firstnegative peak and a positive peak, and wherein the output signalincludes a second inflection between adjacent quarter-cycles forming asegment of the output signal between the positive peak and a secondnegative peak, wherein the first and second inflections represent alevel of said input signal.

In another embodiment a system for generating a modulated signal isprovided that includes a processor configured to generate a thirdharmonic sideband based on a received carrier signal and a receivedinput signal, and to frequency-shift the third harmonic sideband to thefrequency of the received carrier signal.

In yet another embodiment, a system for demodulating a signal isprovided that includes a signal adder for adding a third harmonic to themodulated signal; a peak detector for detecting a peak amplitude of themodulated signal plus third harmonic; a reference ramp generator forgenerating a reference ramp when a peak amplitude is detected; aninflection detector for detecting an inflection in the modulated signalplus third harmonic; and a sample and hold element for sampling thereference ramp when an inflection is detected, and holding andoutputting the sampled value.

In another embodiment, a system for demodulating a signal is providedthat includes a subtraction element for subtracting a fundamentalcarrier signal from a received modulated signal; a fundamental notchfilter for filtering out the fundamental carrier signal, thereby leavingonly the third harmonic component from the modulated signal; and a thirdharmonic phase detector for detecting the phase of the third harmoniccomponent.

In another embodiment, a system for demodulating a signal is providedthat includes an analog to digital converter for converting themodulated signal to a digital signal; and a processor configured toperform a fast Fourier transform on the digital signal.

Embodiments provided by the present disclosure provide a number ofadvantageous features, including:

(1) Modulation generation is from quarter cycle periods compatible witha look-up table as one method—

(2) Modulation generation is compatible with direct sideband generationas one method—

(3) De-modulation process utilizes time domain recreation for subcyclecalibration as one method—

(4) De-modulation process utilizes phase detection of generated thirdharmonic component as one method—

(5) De-modulation process utilizes frequency domain fast Fouriertransform analysis as one method.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe present disclosure, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the disclosure can be better understood with referenceto the following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is an illustration of a TM Modulated signal generated inaccordance with the prior art techniques.

FIG. 2 is a flowchart illustrating a method of modulating a carriersignal, in accordance with a first exemplary embodiment of the presentdisclosure.

FIG. 3 is an illustration of a signal generated as quarter-cycles, inaccordance with an embodiment of the present disclosure.

FIG. 4 is an illustration of the signal shown in FIG. 3 after summingthe quarter-cycles, in accordance with an embodiment of the presentdisclosure.

FIG. 5 is an illustration of an input modulation signal which may beused, by embodiments provided by the present disclosure, to generate thesignal shown in FIG. 4.

FIG. 6 is a plot illustrating the frequency spectrum of the signal shownin FIG. 4.

FIG. 7 is a plot illustrating the frequency spectrum resulting fromheterodyning the third harmonic component with the second harmonic ofthe signal shown in FIG. 6, in accordance with an embodiment provided bythe present disclosure.

FIG. 8 is an illustration of a filter which may be applied toembodiments provided by the present disclosure.

FIG. 9a is a block diagram illustrating a software-based direct spectrumsystem for generating a signal, in accordance with an embodimentprovided by the present disclosure.

FIG. 9b is a block diagram illustrating a hardware-based direct spectrumsystem for generating a signal, in accordance with an embodimentprovided by the present disclosure.

FIG. 10 is a block diagram illustrating a sub-cycle calibration systemfor demodulating a signal, in accordance with an embodiment provided bythe present disclosure.

FIG. 11 is a block diagram illustrating a third harmonic phase detectionsystem for demodulating a signal, in accordance with an embodimentprovided by the present disclosure.

FIG. 12 is a block diagram illustrating a Fast Fourier Transform basedsystem for demodulating a signal, in accordance with an embodimentprovided by the present disclosure.

DETAILED DESCRIPTION

Many embodiments of the disclosure may take the form ofcomputer-executable instructions, including algorithms executed by aprogrammable computer or microprocessor. However, the disclosure can bepracticed with other computer system configurations as well. Certainaspects of the disclosure can be embodied in a special-purpose computeror data processor that is specifically programmed, configured orconstructed to perform one or more of the methods or algorithmsdescribed below.

Aspects of the disclosure described below may be stored or distributedon computer-readable media, including magnetic and optically readableand removable computer disks, fixed magnetic disks, floppy disk drive,optical disk drive, magneto-optical disk drive, magnetic tape, hard-diskdrive (HDD), solid state drive (SSD), compact flash or non-volatilememory, as well as distributed electronically over networks includingthe cloud. Data structures and transmissions of data particular toaspects of the disclosure are also encompassed within the scope of thedisclosure.

FIG. 2 is a flowchart 200 illustrating a method of modulating a carriersignal, in accordance with a first exemplary embodiment of thedisclosure. It should be noted that any process descriptions or blocksin flow charts should be understood as representing modules, segments,portions of code, or steps that include one or more instructions forimplementing specific logical functions in the process, and alternateimplementations are included within the scope of the present inventionin which functions may be executed out of order from that shown ordiscussed, including substantially concurrently in reverse order,depending on the functionality involved, as would be understood by thosereasonably skilled in the art of the present invention. The methodsolves the amplitude variation problem of the prior art (e.g., as shownin FIG. 1 above) and may be implemented in either hardware or software,or any combination thereof. The method shown in FIG. 2, which may bereferred to as the “quarter-cycle assembly” (QC) method, may include aLook-Up-Table (LUT) 210 as a fast method of obtaining the results, thatotherwise may be produced utilizing mathematical functions, without theneed of continuously performing the math. The QC method is based in thetime-domain.

Referring to FIG. 3, the modulated output signal 300 from the methodshown in FIG. 2 includes four distinct quarter cycle segments for eachfull signal cycle. FIG. 3 shows three full cycles (e.g., cycles a, b andc), as may be output by the quarter-cycle method shown in FIG. 2. Eachcycle is composed of four quarter cycle segments (e.g., 301, 302, 303and 304). A gap is shown between quarter cycle segments for illustrativepurposes only. Further, the amplitude positions of the inflections (a1,a2, b1, b2, c1, c2) are exaggerated for illustration purposes. Theinflections are formed between adjacent quarter cycle segments, asshown.

As shown in FIG. 3, the “first” quarter of each cycle (301 a, 301 b and301 c) may have different amplitudes depending on the value of theapplied modulation. The same applies for each other quarter of eachcycle shown. That is, the second (302 a, 302 b, 302 c), third (303 a,303 b, 303 c) and fourth (304 a, 304 b, 304 c) quarters of each cyclemay have different amplitudes depending on the value of the appliedmodulation. When the “first” quarter (e.g., 301 a, 301 b, 301 c) in acycle has a low amplitude, the “second” quarter (e.g., 302 a, 302 b, 302c) of that same cycle has a complimenting higher amplitude so that aconstant amplitude always exists between the negative peak value (Pk⁻)of the whole cycle and the positive peak value (Pk₊) of that cycle. Thesame is true of the “third” and “fourth” quarters of each cycle. Thecauses the positive peak values (Pk₊) of each cycle to always be thesame. The negative peak values (Pk⁻) are also made equal to eliminateamplitude variations due to the applied modulation values.

As is further shown in FIG. 3, the “first” (301 a, 301 b, 301 c) and“third” (303 a, 303 b, 303 c) quarters for a respective cycle have thesame amplitudes. Similarly, the “second” (302 a, 302 b, 302 c) and“forth” (304 a, 304 b, 304 c) quarters for a respective cycle also havethe same amplitudes. The purpose for this is to force the area under thecurve of each cycle to be the same, regardless of applied modulationvalue. This ensures that the average value of each cycle is zero thisavoiding any “DC” value shift in the carrier signal due to the appliedmodulation values.

However, it is noted that for some applications, DC shift may beacceptable, and thus there may be an inconsistent area under the curve,i.e. there need not be symmetry among cycles. In such a case,information or “symbols” may be conveyed at a rate of two symbols percycle, or two different inflection points may be present on each cycle(e.g., one on located along the rising half cycle between the negativepeak and positive peak, and the other located along the falling halfcycle between the positive peak and negative peak).

Each quarter cycle may be generated by a constant clock or time stephence there is no frequency change from one cycle to the next as aresult of the applied modulation value. Each inflection (a1, a2, b1, b2,c1, c2) occurs at precisely the angular equivalent of 180 degreeseparation from one half cycle to the next half cycle. This ensures thatthere is no phase change due to the applied modulation value.

By summing the quarter cycles (e.g., those shown in FIG. 3), a smoothand continuous waveform 300 is obtained, as shown in FIG. 4.

FIG. 5 illustrates a TM modulation signal 500, which is used to producethe modulated signal 300 shown in FIG. 4. As shown in FIGS. 4 and 5,there is one TM Modulation value 500 per carrier cycle. However, asnoted above, there may be two TM Modulation values per carrier cycle inthe case where the cycles may have a different area under curve, i.e.there need not be symmetry among cycles such that you may convey twosymbols on each cycle. In such a case, there could be two TM modulationvalues per carrier cycle, thereby representing two different symbols (orinformation) per carrier cycle. This technique may be suitable fortransmission over optical fiber, for example, because there will be noother signals occupying the transmission bandwidth; however, DC shift istypically not suitable for transmission over other mediums.

A variable designated as the TM Modulation period, t_(TMM), is the timea TM Modulation value is held, and is an integer multiple of the carrierperiod. This would imply that, in such a case, the maximum TM Modulationfrequency, f_(TMM), is one-half of the carrier frequency, f_(C). Thatis, the modulation bandwidth is limited to ½ of f_(C), as it is knownthat the Nyquist rate, or lower bound for the sample rate for alias-freesignal sampling, is two times the bandwidth of a bandlimited signal.However, where two TM modulation values are present per carrier cycle,then the maximum TM modulation frequency, f_(TMM), equals the carrierfrequency, f_(C). There is no minimum value of f_(TMM), including DCresponse. Referring again to FIG. 2, the LUT 210 stores a quarter cycleunique to each value of TM modulation. For each carrier cycle there arefour quarter cycles (e.g., as shown in FIG. 3). If there is anassignment of 1 digital bit (N=1) for each TM Modulation period, thenthere would need to be just two unique TM modulation levels, or twounique sets of two quarter cycles, stored in the LUT 210—one levelsignifying a logic “0” and a second level signifying a logic “1”. Ifthere are two digital bits (N=2) for each t_(TMM) then there would befour levels of potential TM Modulation. Similarly, if there are threebits (N=3) for each t_(TMM), then there would be eight levels of TMModulation, and so on.

The LUT 210 contains 2^(N) different quarter cycle waveshapes or 4*2^(N)total waveshapes, as each full waveshape is composed of 4 quarter cyclewaveshapes. The number of time-steps or clock periods (e.g., theprocessor or CPU clock for reading the LUT 210) per quarter cycle woulddepend on the tolerable waveshape perturbations that the electronics forimplementing the method can tolerate. At carrier frequencies in the 300MHz area, this may require sub-nanosecond time steps. Lower carrierfrequencies may be more amenable to both TM methods (e.g., the LUTbranch and the “math branch,” as described herein) and could beheterodyned up to the carrier frequency.

At block 202, a TM Modulation signal is input to the LUT 210. The TMmodulation signal may be a signal containing, or represented by, anynumber of digital bits (e.g., an N-bits wide signal). The LUT 210contains values or representations for the quarter cycles that mayotherwise be generated by the math branch 220. For example, for each TMmodulation value, which may be represented by rows 210 a (e.g., 1 to2^(N)), a quarter cycle may be associated with the TM modulation valueand stored, represented in columns 210 b, as coordinate data (e.g., x,y)over a period of increasing time (e.g., from an initial time to ¼ of acycle). At block 204, a carrier signal is input having a carrierfrequency of f_(C). The carrier signal may be an RF signal and may serveas a clock signal. At block 206, a decision is made as to whether themodulation will be performed using the LUT 210, or using the math branch220. Either the LUT 210 or the math branch 220 may be utilized togenerate the modulated output signal. If the LUT 210 is utilized, thequarter cycles associated with the received TM modulated values will beoutput from the LUT 210 to the analog gate 208.

If the math branch 220 is utilized, e.g., the math branch 210 isselected from block 206, then the TM modulation signal is input to themath block 220. The math block 220 outputs substantially the samequarter cycle waveforms as would have been output by the LUT block 210for the same received TM modulation values. However, rather than storingthe associated quarter cycle values for each TM modulation value, themath block 220 generates the quarter cycles for each received TMmodulation value. The math block 220 generates the modulated quartercycles by first generating cosine segments of 180° length, at twice thecarrier frequency (2f_(c)), and at the equivalent carrier frequencyquadrants of 0°-90°, 90°-180°, 180°-280°, and 270°-360°. These generatedcosine segments thus make up quarter cycle segments at the carrierfrequency. The amplitude is set by the received TM modulation value forthe 0°-90° and 180°-270° quadrants (i.e., the “first” and “third”quarter cycles), and the compliment modulation value for the 90°-180°and 270°-360° quadrants. It will be readily understood by those havingordinary skill in the relevant art that any sinusoidal signal can begenerated using known mathematical relationships, which may beimplemented in circuits and/or software. Thus, the cosine segments ofthe math branch 220, having an amplitude set by the received TMmodulation value, may be generated accordingly.

The math branch 220 performs math calculations to generate the quartercycle segments using a processor having a clock that is a highermultiple of the carrier frequency—either to execute software code or todrive a hardware-based waveform generator, which may be any knownwaveform generator. It is likely that the math branch 220 would need ahigher clock frequency than the LUT branch 210. The output from eitherthe LUT 210 or the math branch 220 is directed to an analog gate 208that assembles the quarter cycles into one continuous signal and directsit forward to the heterodyne block 212.

For transmission and heterodyne purposes, the frequency domain providesinsight to aspects of this disclosure. FIG. 6 is a plot of the frequencyspectrum of the TM modulated signal 300 shown in FIG. 4, where f_(C) isthe carrier signal frequency, and 2f_(C), 3f_(C), etc. are the second,third, etc. harmonics of the carrier frequency. The signal 300 has thespectrum as shown in FIG. 6 at the point of origin with visibleinflections in some cases.

In addition to the fundamental carrier frequency component 610, there isa third harmonic component 620 of the signal 300 that contains a phasemodulation. TM modulation components are only at the third harmonic,i.e. the TM modulation components are the third harmonic components 620.There is no second harmonic signal. By generating a second harmonicsignal, at block 214, as a local oscillator and using a mixer circuit toheterodyne the third harmonic component, there will be two outputfrequencies: (3f_(C)−2f_(C)) and (3f_(C)+2f_(C)). This is illustrated inFIG. 7. The TM modulation component, i.e., the third harmonic component620, will be shifted down to the fundamental carrier frequency (signal710). The additive component of the heterodyning, i.e., the fifthharmonic component 730, may be filtered out (e.g., by filter 810 shownin FIG. 8) at block 214, and may be filtered to match the output of thedesignated communications channel for transmission.

In contrast to known modulation techniques, as provided by the presentdisclosure the 3rd harmonic is phase shifted, but the phase shift isrelative to the fundamental carrier, not the 3rd harmonic. In normal FMand PM transmissions, what is phase shifted is the carrier itself. TMdoes not alter the fundamental and the 3rd harmonic phase is onlyrelated to the fundamental.

The distinction is important for several reasons. For each half-cycle ofthe fundamental carrier (i.e., each TM modulated Symbol) there are 1.5cycles of the 3rd harmonic with no modulation. There is only a change ofthe 3rd harmonic when the data changes (i.e., when the TM modulationsignal 500 changes). Thus, there is very little impact on power andspectrum, and another reason why we have transparency with conventionalmodulation since in most practical applications, there may be 100 ormore carrier cycles per TM symbol—limited to the communicationchannel—like AM and FM broadcast radio, during which there is no change(i.e., no change of modulation) of the 3rd harmonic. It is simplyshifted in phase (in time) with respect to the fundamental.

Implementation of the QC method requires analog bandwidth that is threeor more times wider than the carrier frequency, as the third harmonic(e.g., 3f_(C)) is utilized. Further, the QC method requires a clockfrequency that is 16 times the carrier signal frequency for just fourtime steps per quarter cycle. QC may be generated at a lower carriersignal and heterodyned upward to the desired carrier frequency. Thelower carrier frequency will dictate the upper frequency limit of the TMModulation value.

FIGS. 9a and 9b are block diagrams illustrating a Direct Spectrum (DS)generation system and method, in a further embodiment of the presentdisclosure. The DS generation method may be a simpler implementation ofthe TM modulation. The DS method generates the sideband spectrumdirectly and adds the energy to whatever else exists within thebandwidth of the communication channel. The DS method is based in thefrequency domain.

Referring to FIG. 6, an existing transmitter has some form of complexmodulation. Typical types of complex modulation in use include QAM,QPSK, OFDM, and so on. The sideband energy of the existing modulation isrepresented by the component 610 in FIG. 6. Adding TM Modulationproduces the third harmonic and the TM sideband energy is represented bythe component 620. Note that a second harmonic component may be presentbut contains no modulation.

The second harmonic signal is valuable in that it can be used to shiftthe TM sideband energy 620 downward to the fundamental carrier frequency610. This is done by heterodyning using a mixer function that multipliestwo sinusoidal input signals together and produces a subtractive and anadditive frequency output. Referring to FIG. 7, the hatching representsthe energy that has been converted from the third harmonic 720 to thefundamental 710 and 5th harmonic 730.

The use of the second harmonic is optional. A phase-locked-loop, asknown in the art, can provide a stable second harmonic. Also, anon-linearity that might exist may actually down-convert some of thesideband energy but may not be stable or a reliable method ofdown-conversion.

Communication regulations require that all transmitters must use anoutput filter to guarantee that no energy be radiated that is outside ofthe designated communication channel. As shown in FIG. 8, an outputfilter 810 may be utilized to eliminate the harmonics for transmissionin the designated communication channel. The filter may include apassband 812.

Utilizing the concepts described above, FIGS. 9a and 9b illustrate twosystems and methods for direct spectrum generation. FIG. 9a illustratesa software-based system and method for direct spectrum generation, whileFIG. 9b illustrates a hardware-based system and method for directspectrum generation. In FIG. 9a a clock signal 910 and a digitalmodulation signal 920 are input to a microprocessor 901. In FIG. 9b acarrier signal 915 and an analog modulation signal 925 are input into anon-linear analog circuit 902. The third harmonic sidebands (e.g., theTM modulation component 620) are directly generated by microprocessor901 and/or circuit 902, based on the input signals. The microprocessor901 and/or circuit 902 further may directly heterodyne the thirdharmonic sideband 620 with the input clock 910 (FIG. 9a ) or carrier 915(FIG. 9b ) to directly create the sideband energy (e.g., 710) at thefundamental frequency. The DS method relies on either softwaregeneration of the overall math expression or non-linear analog circuitsthat execute the math expressions. That is, the microprocessor 901 (FIG.9a ) and/or the circuit 902 (FIG. 9b ) directly computes and generatesthe third harmonic sideband 620 based on the input signals, utilizingknown mathematical relationships. The third harmonic sideband 620 isthen heterodyned by the microprocessor 901 and/or non-linear analogcircuit 902 to shift the third harmonic sideband 620 to the fundamentalfrequency.

Systems and methods for receiving and demodulating TranspositionalModulation will now be disclosed. FIG. 10 is a block diagramillustrating a system a method for demodulating TM modulation signals,which may be referred to as “Sub-Cycle Calibration” (SCC). The SCCdemodulation method of TM Modulation operates in the time domain byreconstruction of the waveform, for example as shown in the QC methodsection (e.g., signal 300 of FIG. 4).

The SCC method adds a third harmonic to the received signal 1001 in awide bandwidth environment. A phase locked loop 1010 generates a preciseand unmodulated third harmonic signal, which is added or multiplied tothe received signal 1001 in element 1020. The voltage levels of eachpositive and negative peak is then detected by positive peak detector1030 and/or negative peak detector 1040 and used to generate a referenceramp (by reference ramp generator 1050) with matching negative andpositive peak values. Thus, at every ½ cycle of the received signal 1001the system (i.e., the occurrence of each peak) is calibrated, as a newreference ramp is generated. The ramp is recreated with each half-cycleof the carrier signal 1001. The timing of the peaks is used by the peaktiming element 1060 to set the timing of the reference ramp. Inflectionsare detected by the detectors 1030 and 1040 and the timing of theinflection is used to sample the reference ramp, output by the referenceramp generator 1050, and hold the sampled ramp value. That voltage isthe TM modulation analog value and is output by the sample and holdelement 1070, and may either be used directly or may be converted todigital. The reference ramp has a positive slope for the negative topositive carrier half cycle. For the next half carrier cycle (i.e., thepositive to negative half cycle), the reference ramp has a negativeslope.

An advantage of the SCC demodulation system and method is that itprovides a robust demodulation technique. This is because SCCdemodulation is concerned only with the occurrence of negative andpositive peaks, and the presence of an inflection between these peaks.As such, SCC demodulation is much less susceptible to errors caused bynoise than other demodulation techniques may be.

FIG. 11 is a block diagram illustrating a demodulation system andmethod, which may be called “Third-Harmonic Phase Detection” (3PD), inaccordance with a further embodiment of the present disclosure. TheThird-Harmonic Phase Detection (3PD) demodulation method of TMModulation operates by regenerating a third harmonic component anddemodulating a phase modulation existing on that component.

As shown in FIG. 11, the received TM modulated signal 1101 is used by aphase-locked loop 1110 to generate a stable, unmodulated fundamentalcarrier signal which is subtracted by subtraction element 1120 from thereceived signal 1101. The output from subtraction element 1120 may befiltered by a fundamental notch filter 1130 to filter out any spuriousemissions at the fundamental carrier frequency. The remaining signal isthus the sideband energy (e.g., the TM modulation component) whichdrives a third harmonic phase detector 1140. The third harmonic phasedetector 1140 may be any known or conventional phase detector. Theresulting output 1150 is the TM modulation analog value.

FIG. 12 is a block diagram illustrating a further demodulation systemand method, in accordance with another embodiment of the presentdisclosure. The demodulation system and method shown in FIG. 12 is aFast Fourier Transform (TMFFT) demodulation method of TM Modulation andoperates by the analysis of the sideband spectrum.

The TMFFT method may provide the most simple hardware implementation;however it may also be the most complex in terms of signal processing.The TM modulated received signal 1201 is analyzed by an FFT function1210 once it has been quantized by an analog-to-digital converter. Oncethe receiver has amplified the signal to a level suitable for conversionto digital bits, the signal is output to an element 1210, which may be aprocessor such as a computer CPU or a more dedicated processor such as aField Programmable Gate Array or any custom integrated circuitspecifically designed to calculate the Fourier Transform. The output ofthe FFT element 1210 is a number of data values representing the signalstrength of the received TM signal 1201 at discrete frequencies. The TMspectrum is known since it relates to the TM mode of operation—thenumber of bits per symbol (i.e. number of assigned bits per TMmodulation period) and the symbol rate.

The symbol rate equals the carrier frequency divided by the number ofcarrier cycles per symbol. Stated mathematically, in an illustrativeexample:1 MHz carrier frequency/10 carrier cycles per symbol=100,000 symbols persecond.

The frequency of the symbol is: 100,000 symbols per second/2=50,000symbol cycles per second.

The frequency of interest in the example thus is 50 kHz, i.e., thesymbol cycle frequency, which is 50 kHz above and below the carrierfrequency. A more accurate FFT demodulation process will also look at100 kHz and 150 kHz to include additional Bessel-related sidebands whenthere are many modulation levels such as 6 bits per symbol or 64modulation levels. Also, when there are just a few carrier cycles persymbol, more sideband frequencies reduces the demodulation error rate.In some receivers the carrier frequency is heterodyned to anintermediate frequency (IF) for amplification or to baseband whichplaces the carrier frequency at zero.

The 50 kHz FFT output value will have a value that follows the TMmodulation. If the TM modulation has 4 bits per symbol, then aconversion from the numerical value of the FFT output, bracketed into 16levels and converted to 4 binary bits produces the TM Modulation value.

It should be emphasized that the above-described embodiments of thepresent disclosure, particularly, any “preferred” embodiments, aremerely possible examples of implementations, merely set forth for aclear understanding of the principles of the disclosure. Many variationsand modifications may be made to the above-described embodiment(s) ofthe disclosure without departing substantially from the spirit andprinciples of the disclosure. All such modifications and variations areintended to be included herein within the scope of this disclosure andthe present disclosure and protected by the following claims.

What is claimed is:
 1. A method of demodulating transpositionalmodulation signals, the method comprising: obtaining a digitalrepresentation of a transpositional modulated signal; performing a fastFourier transform (FFT) on the digital representation of thetranspositional modulated signal to obtain a frequency domainrepresentation of the transpositional modulated signal; identifying atleast one sideband of the transpositional modulated signal in thefrequency domain representation; and detecting a data value of thetranspositional modulated signal in the at least one sideband todemodulate the transpositional modulated signal.
 2. The method of claim1, further comprising determining a symbol rate of the transpositionalmodulated signal, and wherein the at least one sideband is identifiedbased on the symbol rate.
 3. The method of claim 2, wherein the symbolrate of the transpositional modulated signal is determined based on anumber of cycles of a carrier of the transpositional modulated signal onwhich a symbol is represented.
 4. The method of claim 1, whereindemodulating the transpositional modulated signal based on the at leastone sideband comprises: determining a number of sidebands to use fordemodulating the transpositional modulated signal based on a number ofbits per symbol in the transpositional modulated signal; anddemodulating the transpositional modulated signal based the determinednumber of sidebands.
 5. The method of claim 1, wherein a numerical valueof the FFT at the sideband represents the data value of thetranspositional modulated signal.
 6. The method of claim 1, whereindetecting the data value of the transpositional modulated signal in theat least one sideband comprises: bracketing a numerical value of the FFTat the sideband into one of a plurality of levels; and converting thenumerical value into an n-bit binary value represented by the one of theplurality of levels.
 7. A method of demodulating transpositionalmodulation signals, the method comprising: receiving a transpositionalmodulated signal; obtaining an unmodulated signal at a frequency of acarrier signal of the transpositional modulated signal; subtracting theunmodulated signal from the transpositional modulated signal; filteringthe transpositional modulated signal with a notch filter at thefrequency of the carrier signal; and detecting a phase modulation of athird harmonic component of the carrier signal to demodulate thetranspositional modulation signal, wherein the phase modulation of thethird harmonic component represents a TM modulation value.
 8. The methodof claim 7, wherein obtaining the unmodulated signal comprisesgenerating the unmodulated signal using phase-locked loop.
 9. Antranspositional modulation (TM) receiver comprising: means forgenerating a digital representation of a transpositional modulatedsignal from an analog signal; at least one processor in communicationwith the means for generating the digital representation of thetranspositional modulated signal; and a data store coupled to the atleast one processor having instructions stored thereon which, whenexecuted by the at least one processor, causes the at least oneprocessor to perform operations comprising: obtaining the digitalrepresentation of the transpositional modulated signal; performing afast Fourier transform (FFT) on the digital representation of thetranspositional modulated signal to obtain a frequency domainrepresentation of the transpositional modulated signal; identifying atleast one sideband of the transpositional modulated signal in thefrequency domain representation; and detecting a data value of thetranspositional modulated signal in the at least one sideband todemodulate the transpositional modulated signal.
 10. The receiver ofclaim 9, wherein the operations further comprise determining a symbolrate of the transpositional modulated signal, and wherein the at leastone sideband is identified based on the symbol rate.
 11. The receiver ofclaim 10, wherein the symbol rate of the transpositional modulatedsignal is determined based on a number of cycles of a carrier of thetranspositional modulated signal on which a symbol is represented. 12.The receiver of claim 9, wherein demodulating the transpositionalmodulated signal based on the at least one sideband comprises:determining a number of sidebands to use for demodulating thetranspositional modulated signal based on a number of bits per symbol inthe transpositional modulated signal; and demodulating thetranspositional modulated signal based the determined number ofsidebands.
 13. The receiver of claim 9, wherein a numerical value of theFFT at the sideband represents the data value of the transpositionalmodulated signal.
 14. The receiver of claim 9, wherein detecting thedata value of the transpositional modulated signal in the at least onesideband comprises: bracketing a numerical value of the FFT at thesideband into one of a plurality of levels; and converting the numericalvalue into an n-bit binary value represented by the one of the pluralityof levels.
 15. The receiver of claim 9, wherein the means for generatinga digital representation of a transpositional modulated signal from ananalog signal is an analog-to-digital converter.